[om-list] Coin Tossing Theory

[Mark Butler]

Suppose that you, having no prior knowledge of coins, have someone come 
up to you and say through experimental research he has determined that 
tossed coins always end up heads. 

Having a skeptical mind and a curious bent, you decide to test his 
theory through experiment. Of course, on average the coin ends up heads 
only about half the time.  There are a couple of ways you might treat 
this data:

    Conventional Boolean logic:

    Each time the coin toss is heads, it adds a small amount of
    confirming evidence for the hypothesis.  The first time the coin
    toss is tails, that adds a sufficient amount of disconfirming
    evidence to disprove the theory.  You remark on the correctness of
    the maxim, "All generalizations are false".  You are convinced that
    the theory has no likelihood of being right. Your degree of belief
    in his theory is "absolutely false".

    Fuzzy logic:

    You tally up the net number of heads and the net number of tails,
    divide, get a number near 1/2 and conclude, "I am confident he is
    half right, after all he could have been wrong all the time.  Your
    degree of belief in his theory remains neutral on a scale ranging
    between "always wrong" and "always right".

Given the presence of minor errors in most theories, I submit that fuzzy 
logic is much more appropriate for estimating truth values of 
propositions in a semantic network than traditional Boolean logic.  With 
the latter, we have to toss out a theory completely on the first 
inconsistency.  It is much more useful to track the predictive value of 
propositions, that like all generalizations admit of exceptions, as a 
continuous variable, even when the subject data is boolean in nature, as 
in the example.

It drives me crazy to hear people claim that Quantum Mechanics implies 
that Newton's Laws are now "false", when in actuality they are extremely 
accurate on a very wide scale of applicability. 

 - Mark






-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://six.pairlist.net/pipermail/om-list/attachments/20030829/45a1d30f/attachment.html